# Thread: Am I missing a step? quoitent rule

1. ## Am I missing a step? quoitent rule

I have to differentiate the following:

$f(x)=\frac{2}{ 3x-2 }$

Alright simple enough so i follow the quotient rule for this question:

$f(x)=\frac{g(x)\cdot f'(x) - f(x)\cdot (g'(x)}{[g(x)]^2 }$

$\frac{(3x-2)(0)-(2)(3)}{(3x-2)^2 }$
$\frac{(3x-2)-6}{(3x-2)^2 }$

When i check the answer in mathway it says it should be :

$-\frac{6}{(3x-2)^2 }$

So not really sure about what happens to the 3x-2? is the question still right if you only get to:

$\frac{(3x-2)-6}{(3x-2)^2 }$

2. Originally Posted by sara213
I have to differentiate the following:

$f(x)=\frac{2}{ 3x-2 }$

Alright simple enough so i follow the quotient rule for this question:

$f(x)=\frac{g(x)\cdot f'(x) - f(x)\cdot (g'(x)}{[g(x)]^2 }$

$\frac{(3x-2)(0)-(2)(3)}{(3x-2)^2 }$
What is 0 times (3x-2)?

$\frac{(3x-2)-6}{(3x-2)^2 }$

When i check the answer in mathway it says it should be :

$-\frac{6}{(3x-2)^2 }$

So not really sure about what happens to the 3x-2? is the question still right if you only get to:

$\frac{(3x-2)-6}{(3x-2)^2 }$

3. Originally Posted by sara213
I have to differentiate the following:

$f(x)=\frac{2}{ 3x-2 }$

Alright simple enough so i follow the quotient rule for this question:

$f(x)=\frac{g(x)\cdot f'(x) - f(x)\cdot (g'(x)}{[g(x)]^2 }$

$\frac{(3x-2)(0)-(2)(3)}{(3x-2)^2 }$
$\frac{(3x-2)-6}{(3x-2)^2 }$

When i check the answer in mathway it says it should be :

$-\frac{6}{(3x-2)^2 }$

So not really sure about what happens to the 3x-2? is the question still right if you only get to:

$\frac{(3x-2)-6}{(3x-2)^2 }$
I'd use the chain rule and exponent laws rather than quotient rule

$f(x) = 2(3x-2)^{-1}$

$f'(x) = 2 \cdot \dfrac{d}{dx}(3x-2)^{-1} \cdot \dfrac{d}{dx}(3x) = \dfrac{6}{(3x-2)^2}$

4. Originally Posted by e^(i*pi)
I'd use the chain rule and exponent laws rather than quotient rule

$f(x) = 2(3x-2)^{-1}$

$f'(x) = 2 \cdot \dfrac{d}{dx}(3x-2)^{-1} \cdot \dfrac{d}{dx}(3x) = \dfrac{6}{(3x-2)^2}$
It's six of one, a half-dozen of the other. I find that the quotient rule, while a little more work up front, can save algebra later, since you don't have to get common denominators and add fractions (in case the numerator is more complicated than in the present problem).